A semi-analytical modeling method for kinematics of a humanoid wrist parallel mechanism and a terminal

Abstract

The application discloses a kind of kinematics semi-analytical modeling method and terminal of humanoid wrist parallel mechanism, method includes: when kinematics positive solution is carried out to wrist parallel mechanism, global coordinate system, first coordinate system and second coordinate system are constructed, then the end pose of the parallel mechanism of the humanoid wrist corresponding to target D H Expression, the target D H Expression shows the relationship between the end pose and first joint angle, second joint angle, then target module length expression is acquired, the target module length expression shows the relationship between first module length and second module length and the first joint angle and the second joint angle, finally, the numerical value of first module length and second module length is acquired, the numerical value of the first module length and the second module length is brought into the target D H Expression and the target module length expression, to acquire end pose.The application provides a solution for humanoid wrist parallel mechanism, which can be operated on a low-power platform.​​​

Description

Technical Field

[0001] This invention relates to the field of linkage processing, and in particular to a kinematic semi-analytical modeling method and terminal for a parallel mechanism that mimics a human wrist. Background Technology

[0002] With the continuous development of robotics technology, people have put forward increasingly complex requirements for various types of robotic arm technologies. Taking the development of humanoid robots as an example, it has placed further demands on the appearance and function of humanoid robotic arms.

[0003] Humanoid robotic arms are mainly divided into two categories: serial robotic arms and hybrid robotic arms. Traditional serial robotic arms typically use several rotary motors connected in series to form an arm with 6 or 7 degrees of freedom. This design makes the robotic arm relatively simple in structure, computation, and control. However, this serial mechanism suffers from weak rigidity. This is because the end joints of the robotic arm have continuous stacking, leading to increased end-effector inertia.

[0004] Parallel mechanisms can effectively solve the aforementioned problems. They are characterized by high end-effector stiffness and accurate motion. Furthermore, parallel mechanisms are not limited to rotary joints; they can utilize linear drives with lower inertia to achieve upward displacement of inertia. However, parallel mechanisms also have some drawbacks: they are difficult to calculate, involve motion coupling, and their operating range is typically much smaller than that of serial mechanisms.

[0005] For humanoid robotic arms, the wrist generally does not require a large workspace, but it does require high precision and rigidity (for stress). Therefore, using a parallel mechanism in the wrist joint can achieve more ideal results.

[0006] However, while the inverse kinematics of parallel mechanisms is relatively easy, the forward kinematics solution is often quite difficult, sometimes even impossible to compute analytically. Simple numerical iteration generally relies on iterative algorithms, which are computationally slow and prone to getting trapped in local optima. Currently, there is no forward kinematics method for parallel mechanisms in anthropomorphic wrists.

[0007] Therefore, there is an urgent need for a kinematic analytical or semi-analytical method for parallel mechanisms of human wrists to quickly solve the kinematic characteristics of parallel mechanisms of human wrists.

[0008] Therefore, existing technologies still need to be improved and enhanced. Summary of the Invention

[0009] To address the aforementioned deficiencies in existing technologies, this invention provides a parallel mechanism for a human wrist and a semi-analytical kinematic modeling method thereof. This aims to solve the problem that existing technologies lack analytical or semi-analytical kinematic methods for parallel mechanisms of a human wrist, thus hindering the rapid solution of the motion characteristics of such mechanisms.

[0010] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0011] A first aspect of the present invention provides a semi-analytical kinematic modeling method for a parallel mechanism of a human wrist, applied to a parallel mechanism of a human wrist. When performing forward kinematic analysis on the parallel mechanism of the human wrist, the method includes:

[0012] Obtain a global coordinate system, a first coordinate system, and a second coordinate system. The global coordinate system is the overall coordinate system of the parallel mechanism of the humanoid wrist. The origin of the first coordinate system is the rotation center of the first rotary joint of the parallel mechanism of the humanoid wrist. z The axis coincides with the rotation axis of the first rotary joint; the origin of the second coordinate system is the rotation center of the second rotary joint of the parallel mechanism of the anthropomorphic wrist, and the second coordinate system... z The shaft coincides with the rotation axis of the second rotary joint;

[0013] Obtain the target corresponding to the end-effector pose of the parallel mechanism of the humanoid wrist. D - H The expression, the target D - H The expression illustrates the relationship between the end-effector pose and the first joint angle and the second joint angle, where the first joint angle is the angle of the third branch of the parallel mechanism of the anthropomorphic wrist around the first coordinate system. z The angle of rotation of the axis, the second joint angle is the angle of rotation of the third branch around the second coordinate system. z The angle of axis rotation, wherein the third branch is used to connect the active drive branch of the parallel mechanism of the humanoid wrist and the moving platform of the parallel mechanism of the humanoid wrist, and the active drive branch includes the first branch and the second branch.

[0014] Obtain the target module length expression, which shows the relationship between the first module length and the second module length and the first joint angle and the second joint angle. The first module length is the module length of the first vector in the global coordinate system, and the second module length is the module length of the second vector in the global coordinate system. The first vector is the vector representation of the first branch, and the second vector is the vector representation of the second branch.

[0015] Obtain the values ​​of the first module length and the second module length, and substitute these values ​​into the target. D - H The expression and the target module length expression are used to obtain the end pose.

[0016] In a second aspect, the present invention provides a terminal comprising a processor and a computer-readable storage medium communicatively connected to the processor, the computer-readable storage medium being adapted to store a plurality of instructions, the processor being adapted to invoke the instructions in the computer-readable storage medium to perform the steps of the kinematic semi-analytical modeling method for implementing the parallel mechanism of the anthropomorphic wrist as described in any of the preceding claims.

[0017] Compared with existing technologies, this invention provides a semi-analytical kinematic modeling method and terminal for a parallel mechanism of a human wrist. The semi-analytical kinematic modeling method for the parallel mechanism of the human wrist obtains a global coordinate system, a first coordinate system, and a second coordinate system when performing forward kinematics on the parallel mechanism of the human wrist. The global coordinate system is the overall coordinate system of the parallel mechanism of the human wrist, and the origin of the first coordinate system is the rotation center of the first revolute joint of the parallel mechanism of the human wrist. z The axis coincides with the rotation axis of the first rotary joint; the origin of the second coordinate system is the rotation center of the second rotary joint of the parallel mechanism of the anthropomorphic wrist, and the second coordinate system... z The axis coincides with the rotation axis of the second rotary joint. Then, the target corresponding to the end pose of the parallel mechanism of the humanoid wrist is obtained. D - H The expression, the target D - H The expression illustrates the relationship between the end-effector pose and the first joint angle and the second joint angle, where the first joint angle is the angle of the third branch of the parallel mechanism of the anthropomorphic wrist around the first coordinate system. z The angle of rotation of the axis, the second joint angle is the angle of rotation of the third branch around the second coordinate system. zThe angle of axis rotation, wherein the third branch is used to connect the active drive branch of the parallel mechanism of the humanoid wrist and the moving platform of the parallel mechanism of the humanoid wrist. The active drive branch includes a first branch and a second branch. Then, the target modulus expression is obtained. The target modulus expression shows the relationship between the first modulus and the second modulus and the first joint angle and the second joint angle. The first modulus is the modulus of the first vector in the global coordinate system, and the second modulus is the modulus of the second vector in the global coordinate system. The first vector is the vector representation of the first branch, and the second vector is the vector representation of the second branch. Finally, the values ​​of the first modulus and the second modulus are obtained, and the values ​​of the first modulus and the second modulus are substituted into the target... D - H The expression and the target modulus expression are used to obtain the end-effector pose. The semi-analytical kinematic modeling method for parallel mechanisms of anthropomorphic wrists proposed in this invention solves the problem that existing technologies lack analytical or semi-analytical kinematic methods for parallel mechanisms of anthropomorphic wrists, making it impossible to quickly solve for the motion characteristics of such mechanisms. For the first time, a 2... SPS - RR The semi-analytical kinematic modeling of the mechanism proposes a semi-analytical kinematic expression for the parallel mechanism of the human wrist. Through this semi-analytical form, we can observe the equations to know which factors affect the final result, bringing a more intuitive understanding to the solution. Attached Figure Description

[0018] Figure 1 A flowchart illustrating an embodiment of the kinematic semi-analytical modeling method for the parallel mechanism of the human wrist provided by the present invention;

[0019] Figure 2 A structural diagram of the parallel mechanism for the human wrist provided by the present invention;

[0020] Figure 3 A schematic diagram illustrating the principle of an embodiment of the terminal provided by the present invention. Detailed Implementation

[0021] To make the objectives, technical solutions, and effects of this invention clearer and more explicit, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0022] Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in this specification means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. It should be understood that when we say an element is “connected” or “coupled” to another element, it can be directly connected or coupled to the other element, or there may be intermediate elements. Furthermore, “connected” or “coupled” as used herein can include wireless connections or wireless coupling. The term “and / or” as used herein includes all or any units and all combinations of one or more associated listed items.

[0023] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless specifically defined as herein.

[0024] The kinematic semi-analytical modeling method for parallel mechanisms of anthropomorphic wrists provided by this invention can be applied to terminals with computing capabilities. The terminal can execute the kinematic semi-analytical modeling method for parallel mechanisms of anthropomorphic wrists provided by this invention to perform kinematic modeling and analysis of parallel mechanisms of anthropomorphic wrists.

[0025] Example 1

[0026] This embodiment is a semi-analytical kinematic modeling method for a parallel mechanism that mimics a human wrist. The semi-analytical kinematic modeling method for the parallel mechanism that mimics a human wrist can be executed by a terminal, which can be, but is not limited to, smart devices, computers, etc. The following description uses a computer as an example.

[0027] In this embodiment, through improvement D - H ( Modified Denavit - Hartenberg , MDH The method is used to model the parallel mechanism of the anthropomorphic wrist.

[0028] Specifically, for parallel mechanisms, the inverse kinematics solution is relatively easy, but the forward kinematics solution is often quite difficult, even impossible to calculate analytically. Simple numerical iteration generally relies on iterative algorithms, which are slow and prone to getting trapped in local optima. Currently, there are no clear analytical or semi-analytical algorithms for this type of wrist mechanism. If only numerical solutions are relied upon, without specific modeling of the parallel wrist mechanism, computational efficiency cannot be guaranteed, causing difficulties in the use of robotic arms in highly dynamic and high-accuracy applications.

[0029] In other words, purely numerical solutions are slow and require certain computational performance. Purely analytical solutions are also difficult to calculate. Therefore, this embodiment proposes a semi-analytical solution method. It still performs mathematical and mechanical modeling of the parallel mechanism of the anthropomorphic wrist. Then, based on the characteristics of kinematic mathematics, completely unrelated variables are simplified into a simple system of nonlinear equations through mathematical transformations. By using variable substitution and dimensionality reduction, a new, easily solvable system of nonlinear equations is constructed. This allows for rapid solution even with lower computational power.

[0030] Specifically, such as Figure 1 As shown, in one embodiment of the kinematic semi-analytical modeling method for a parallel mechanism of a human wrist provided by the present invention, the kinematic semi-analytical modeling method for a parallel mechanism of a human wrist is applied to a parallel mechanism of a human wrist, and the steps included in performing forward kinematic solution for the parallel mechanism of the human wrist are as follows:

[0031] S 100. Obtain the global coordinate system, the first coordinate system, and the second coordinate system, wherein the global coordinate system is the total coordinate system of the parallel mechanism of the humanoid wrist, the origin of the first coordinate system is the rotation center of the first rotary joint of the parallel mechanism of the humanoid wrist, and the first coordinate system... z The axis coincides with the rotation axis of the first rotary joint; the origin of the second coordinate system is the rotation center of the second rotary joint of the parallel mechanism of the anthropomorphic wrist, and the second coordinate system... z The shaft coincides with the rotation axis of the second rotary pair.

[0032] Specifically, refer to Figure 2 In this embodiment, the parallel mechanism of the humanoid wrist includes a support, a first branch, a second branch, a third branch, and a moving platform.

[0033] Both the first and second branches include a front ball joint, a sliding joint, and a rear ball joint. The front ball joints of both the first and second branches are connected to the support, and the rear ball joints of both the first and second branches are connected to the third branch. The sliding joints of the first and second branches are active driving components, and the center point of the front ball joint of the first branch is... A Point, the rear spherical subcenter point of the first branch is C Point; the center point of the front end sphere of the second branch is B Point, the rear spherical subcenter point of the second branch is D point;

[0034] The third branch includes a first revolute joint and a second revolute joint. The second revolute joint is connected to the moving platform, and the center of rotation of the second revolute joint is the geometric center of the moving platform. The center of rotation of the first revolute joint is... F Point, the center of rotation of the second revolute joint is G point;

[0035] The moving platform is the output end of the parallel mechanism of the humanoid wrist.

[0036] The first branch and the second branch are both ball joint-moving joint-ball joint structures, and the third branch is a revolute joint-revolute joint structure.

[0037] Specifically, in this embodiment, the parallel mechanism of the humanoid wrist is two components of the humanoid wrist. SPS - RR Parallel mechanisms. Among them, S Representative ball vice ( Sphericaljoint ), P Represents the moving sub-unit ( Prismaticjoint ), R Represents a revolute joint ( Rotationaljoint The specific structure is as follows: Figure 2 As shown.

[0038] The parallel mechanism of the anthropomorphic wrist specifically consists of a support, three branches, and a moving platform. The first and second branches are connected in a "ball joint-prismatic joint-ball joint" relationship, while the third branch is connected in a "revolute joint-revolute joint" relationship. Therefore, in this embodiment, the parallel mechanism of the anthropomorphic wrist is also referred to as 2. SPS - RR mechanism.

[0039] Specifically, refer to Figure 2 , The coordinate system for the entire parallel mechanism of the humanoid wrist, referred to in this embodiment as the global coordinate system, is... Figure 2 In the diagram, the red arrows indicate the coordinate system.x Direction, indicated by the blue arrow. z Direction, indicated by the green arrow. y Direction. The moving platform is the output end of the parallel mechanism of the anthropomorphic wrist. In specific driving, the moving joints of the first and second branches are active drives, while the third branch is a passive branch and does not have the ability to be actively driven. Figure 2 In this context, the revolute joint of the third branch includes the first revolute joint. and the second rotary joint Corresponding to the first rotary joint Establish the first coordinate system, corresponding to the second rotational joint. Establish a second coordinate system. Specifically, in this embodiment, the first coordinate system... The origin and orientation are used F Point representation, that is, the origin of the first coordinate system is the point. F Point, its z The axis coincides with the rotation axis of the first rotary joint, and the second coordinate system The origin and orientation are used F Point representation, that is, the origin of the second coordinate system is the point represented by the point. G Point, its z The axis coincides with the rotation axis of the second rotary joint. It is worth noting that although the parallel mechanism has the characteristic of motion coupling, the motion of the end of the parallel mechanism of the anthropomorphic wrist in this embodiment can be characterized by the rotation angle of the passive branch.

[0040] After constructing the global coordinate system, the first coordinate system, and the second coordinate system, the following steps are also included:

[0041] S 200. Obtain the target position corresponding to the end effector pose of the parallel mechanism of the humanoid wrist. D - H The expression, the target D - H The expression illustrates the relationship between the end-effector pose and the first joint angle and the second joint angle, where the first joint angle is the angle of the third branch of the parallel mechanism of the anthropomorphic wrist around the first coordinate system. z The angle of rotation of the axis, the second joint angle is the angle of rotation of the third branch around the second coordinate system. z The angle of axis rotation, wherein the third branch is used to connect the active drive branch of the parallel mechanism of the humanoid wrist and the moving platform of the parallel mechanism of the humanoid wrist, the active drive branch including the first branch and the second branch.

[0042] Specifically, in this embodiment, the system is based on an improved version. D -H ( Modified Denavit - Hartenberg , MDH The parallel mechanism of the anthropomorphic wrist is modeled using the following method. D - H The parameter table is shown in Table 1:

[0043] Table 1:

[0044]

[0045] Specifically, the sliding joints of the first and second branches, i.e., the links, are characterized by four key parameters:

[0046] Indicates the length of the link, referring to the length along the current coordinate system. x The distance between the axes of two joints measured in the axial direction;

[0047] Indicates the link twist angle, referring to the angle about the current coordinate system. x The angle of rotation of the axis is used to adjust the next coordinate system. z Axial direction;

[0048] Indicates the link offset, referring to the offset along the current coordinate system. z The perpendicular distance from the axis direction to the origin of the next coordinate system;

[0049] Indicates the joint angle of the link, referring to the angle about the current coordinate system. Z The angle of rotation of the shaft determines the relative orientation between adjacent links.

[0050] exist D - H In the parameter table, except and All others are fixed, known values.

[0051] In the inverse kinematics of a parallel mechanism, it is equivalent to knowing... Solve for the moving joint AC and BD The length of the vector can be relatively easily represented by pose transformation. The forward kinematics of the parallel mechanism of the anthropomorphic wrist described in this embodiment is based on the known modulus fields of two vectors. and Solving for the coordinate system In wrist coordinate system The following expression Also known as the end effector pose, it refers to the position and orientation of the robot's end effector relative to the base coordinate system.

[0052] Specifically, first based on the improvementsD - H Modeling methods, list expression:

[0053] ;

[0054] Since the secondary transformation matrix between rigid bodies can be expressed as:

[0055] ;

[0056] Based on this and All can be based on D - H The expression is written out, so the target of the end pose is... D - H The expression is:

[0057] ;

[0058] in, 1 represents the global coordinate system, and 2 represents the second coordinate system. The end-effector pose represents the position and orientation of the moving platform relative to the global coordinate system. express , express , Indicates along the second coordinate system x The distance between the axes of the first and second revolute joints, measured in the axial direction. The first joint angle, This is the second joint angle.

[0059] S 300. Obtain the target modulus expression, which shows the relationship between the first modulus and the second modulus and the first joint angle and the second joint angle. The first modulus is the modulus of the first vector in the global coordinate system, and the second modulus is the modulus of the second vector in the global coordinate system. The first vector is the vector representation of the first branch, and the second vector is the vector representation of the second branch.

[0060] The process of obtaining the target modulus expression includes:

[0061] S 310. Based on the stated objective D - HThe expression yields a first vector expression and a second vector expression. The first vector expression shows the relationship between the first vector and the first joint angle and the second joint angle, and the second vector expression shows the relationship between the second vector and the first joint angle and the second joint angle.

[0062] Based on the target D - H The expressions construct the first vector expression and the second vector expression, including:

[0063] S 311. Based on the stated objective D - H Expression retrieval A point, B point, C Point and D The position matrix of the point in the global coordinate system, wherein, A The point is the center point of the ball joint connecting the first branch and the support of the parallel mechanism of the anthropomorphic wrist. B The point is the center point of the ball joint connecting the second branch and the support of the parallel mechanism of the anthropomorphic wrist. C The point is the center point of the spherical joint connecting the first branch and the third branch. B The point is the center point of the sphere connecting the second branch and the third branch.

[0064] Based on the target D - H Expression retrieval A point, B point, C Point and D The position matrix of a point in the global coordinate system includes:

[0065] The A The position matrix of the point in the global coordinate system is:

[0066] ;

[0067] The B The position matrix of the point in the global coordinate system is:

[0068] ；

[0069] The C The position matrix of the point in the global coordinate system is:

[0070] ;

[0071] in, , for the C The position matrix of the point in the second coordinate system;

[0072] The D The position matrix of the point in the global coordinate system is:

[0073] ;

[0074] in, , for the D The position matrix of the point in the second coordinate system, and ; .

[0075] Specifically, refer to Figure 2 It can be seen that the above A Points and the above B The point in the global coordinate system The position in is fixed, therefore the aforementioned can be set. A The position matrix of the point in the global coordinate system is: The B The position matrix of the point in the global coordinate system is: The above C Points and the above D Point in the second coordinate system The position in is fixed, therefore the aforementioned can be set. C The position matrix of the point in the second coordinate system is: The D The position matrix of the point in the second coordinate system is: And it can be seen that, , .

[0076] Then, based on the stated objective D - H The expressions respectively obtain the C Points and the above D The position matrix of the point in the global coordinate system:

[0077] ;

[0078] .

[0079] S 312. Based on the above A Points and the above C The position matrix of the point in the global coordinate system yields the first vector expression;

[0080] S313. Based on the above B Points and the above D The position matrix of the point in the global coordinate system yields the second vector expression.

[0081] Specifically, the vector representation between two points is determined based on the positions of the two points; therefore, the expression for the first vector is:

[0082] ;

[0083] The second vector expression is:

[0084] .

[0085] The above obtained the first vector, the second vector, and the unknown variable. and Next, we need to obtain the relationship between the first vector and the first modulus, and the relationship between the second vector and the second modulus, so as to find the relationship between the first modulus and the second modulus and the first joint angle and the second joint angle.

[0086] S 320. Obtain the first relation and the second relation, wherein the first relation represents the relationship between the first modulus and the first vector, and the second relation represents the relationship between the second modulus and the second vector.

[0087] Specifically, the magnitude usually refers to the magnitude of the vector ( magnitude ), or length, is a scalar value describing the size of a vector. Therefore, the relationship between a vector and its corresponding magnitude can be expressed by a formula.

[0088] The first relation is:

[0089] ;

[0090] The second relation is:

[0091] ;

[0092] in, Indicates the length of the first module. This indicates the length of the second module.

[0093] S 330. Obtain the target modulus expression based on the first vector expression, the second vector expression, the first relation, and the second relation.

[0094] The step of obtaining the target modulus expression based on the first vector expression, the second vector expression, the first relation, and the second relation includes:

[0095] The first intermediate relation is obtained based on the first relation and the second relation;

[0096] Optimizing the first intermediate relation yields the second intermediate relation:

[0097] The target modulus expression is obtained based on the second intermediate relation.

[0098] The first intermediate relation is:

[0099] ;

[0100] ;

[0101] The second intermediate relation is:

[0102] ;

[0103] .

[0104] The step of obtaining the target modulus expression based on the second intermediate relation includes:

[0105] The second intermediate relation is adjusted based on the target constant coefficients to obtain the target modulus expression. Specifically, multiple target constant coefficients are added to the second relation, and then combined to obtain the following relation:

[0106] ;

[0107] .

[0108] in, and All are constant coefficients. k =1, 2, 3, ..., 9, representing the following:

[0109] ;

[0110] ;

[0111] because and Therefore, the coefficient All of these can be eliminated. Furthermore, due to the characteristics of the system... ,so Therefore, by simplifying the relation, we obtain the expression for the target modulus:

[0112] .

[0113] S 400. Obtain the values ​​of the first module length and the second module length, and substitute the values ​​of the first module length and the second module length into the target. D - H The expression and the target module length expression are used to obtain the end pose.

[0114] Specifically, the left side of the target modulus expression consists of known quantities, while the right side contains unknown quantities. and Therefore, the original complex system of equations is transformed into a simple system of two linear nonlinear equations.

[0115] Since the expression for the target modulus cannot be further simplified, a numerical solver is used to obtain the result. and When the result is found and Then, the target can be utilized. D - H The expression expresses This allows for the calculation of the forward kinematics solution.

[0116] Specifically, the kinematic semi-analytical modeling method of the parallel mechanism of the human wrist described in this embodiment eliminates a large number of parameters, greatly simplifies the equation system, and transforms it into a simple nonlinear equation system, which can then be solved using general numerical solution tools.

[0117] For the second relation after simplification and merging, the given conditions of the forward kinematics solution are... and The modulus length, then and Since the sum and difference of squares are also known quantities, the left side of the second relation is a known quantity, while the unknown quantity on the right side is only... and , and Since all coefficients are constants, this system of equations has two equations and two unknowns, and can be solved. and Then, based on the target representing the end-effector pose... D - H Expression for solving end-effector pose This completes the calculation of the forward kinematics.

[0118] In this embodiment, the inverse kinematics solution of the parallel mechanism of the humanoid wrist is also included, because it is a parallel mechanism and its inverse kinematics solution is relatively simple.

[0119] Specifically, the inverse solution of the parallel mechanism of the humanoid wrist is performed by giving the end-effector pose. Find and The length of the vector is the magnitude of the vector, which is the first magnitude and the second magnitude.

[0120] Specifically, because of the stated C Points and the above D The point relative to the moving platform G The position of the point is fixed, so the stated C Points and the above D Point in the second coordinate system The coordinates can be represented as:

[0121] ;

[0122] ;

[0123] And the following relationship is satisfied: .

[0124] Therefore, if it is known Then we have:

[0125] ;

[0126] In the formula above, everything on the left side of the equal sign is a known quantity, and everything on the right side is a quantity that needs to be calculated.

[0127] Meanwhile, the A Points and the above B The point in the global coordinate system The coordinate system is also fixed and known, that is:

[0128] ;

[0129] And satisfy the relationship ;

[0130] Therefore, vector and It can be represented as:

[0131] ;

[0132] This formula can be used to express vectors. and .

[0133] Then, using the modulus formulas, namely the first relation and the second relation:

[0134] ;

[0135] ;

[0136] The inverse solution of the parallel mechanism of the humanoid wrist can then be completed.

[0137] In the existing technology, for this type of 2 SPS - RR While no analytical or semi-analytical solution based on analytical methods has been proposed for parallel mechanisms, this embodiment utilizes mathematical symmetry to fully represent the forward and inverse kinematics of the anthropomorphic wrist parallel mechanism and provides analytical expressions. This allows for millisecond-level computations with relatively low computing power, creating conditions for real-time control of the mechanism. The initial value is 2... SPS - RR Parallel mechanisms provide a semi-analytical solution that can perform millisecond-level calculations on low-computing-power platforms.

[0138] Furthermore, this embodiment provides an analytical expression. Compared to directly using numerical tools, which only require inputting equations and can then solve the problem iteratively, this approach avoids the fact that the factors influencing the result are completely unknown during the solution process. However, through this semi-analytical form, after simplification to its simplest form, one can observe the equations to understand which factors affect the final result, providing a more intuitive understanding of the solution process.

[0139] In summary, this embodiment provides a semi-analytical kinematic modeling method for a parallel mechanism of a human wrist. This method, when performing forward kinematics on the parallel mechanism of the human wrist, obtains a global coordinate system, a first coordinate system, and a second coordinate system. The global coordinate system is the overall coordinate system of the parallel mechanism of the human wrist. The origin of the first coordinate system is the rotation center of the first revolute joint of the parallel mechanism of the human wrist. z The axis coincides with the rotation axis of the first rotary joint; the origin of the second coordinate system is the rotation center of the second rotary joint of the parallel mechanism of the anthropomorphic wrist, and the second coordinate system... z The axis coincides with the rotation axis of the second rotary joint. Then, the target corresponding to the end pose of the parallel mechanism of the humanoid wrist is obtained. D - H The expression, the target D - H The expression illustrates the relationship between the end-effector pose and the first joint angle and the second joint angle, where the first joint angle is the angle of the third branch of the parallel mechanism of the anthropomorphic wrist around the first coordinate system. zThe angle of rotation of the axis, the second joint angle is the angle of rotation of the third branch around the second coordinate system. z The angle of axis rotation, wherein the third branch is used to connect the active drive branch of the parallel mechanism of the humanoid wrist and the moving platform of the parallel mechanism of the humanoid wrist. The active drive branch includes a first branch and a second branch. Then, the target modulus expression is obtained. The target modulus expression shows the relationship between the first modulus and the second modulus and the first joint angle and the second joint angle. The first modulus is the modulus of the first vector in the global coordinate system, and the second modulus is the modulus of the second vector in the global coordinate system. The first vector is the vector representation of the first branch, and the second vector is the vector representation of the second branch. Finally, the values ​​of the first modulus and the second modulus are obtained, and the values ​​of the first modulus and the second modulus are substituted into the target... D - H The expression and the target modulus expression are used to obtain the end-effector pose. The semi-analytical kinematic modeling method for parallel mechanisms of anthropomorphic wrists proposed in this embodiment solves the problem that existing technologies lack analytical or semi-analytical kinematic methods for parallel mechanisms of anthropomorphic wrists, making it impossible to quickly solve for the motion characteristics of parallel mechanisms of anthropomorphic wrists. For the first time, a 2... SPS - RR The semi-analytical kinematic modeling of the mechanism proposes a semi-analytical kinematic expression for the parallel mechanism of the human wrist. Through this semi-analytical form, we can observe the equations to know which factors affect the final result, bringing a more intuitive understanding to the solution.

[0140] It should be understood that although the steps in the flowcharts shown in the accompanying drawings are displayed sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowchart may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least a portion of the sub-steps or stages of other steps.

[0141] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided by this invention can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM). ROM Programmable ROM ( PROM ), electrically programmable ROM ( EPROM Electrically erasable programmable ROM ( EEPROM ) or flash memory. Volatile memory may include random access memory (RAM) RAM Alternatively, an external cache memory. This is for illustrative purposes only and not as a limitation. RAM It can be obtained in various forms, such as static RAM ( SRAM ),dynamic RAM ( DRAM ),synchronous DRAM ( SDRAM ), double data rate SDRAM ( DDR SDRAM ), Enhanced SDRAM ( ESDRAM ), Synchronization Link ( Synchlink ), DRAM ( SLDRAM ), memory bus ( Rambus )direct RAM ( RDRAM ), Direct Memory Bus Dynamics RAM ( DRDRAM ), and memory bus dynamics RAM ( RDRAM )wait.

[0142] Example 2

[0143] Based on the above embodiments, the present invention also provides a terminal, such as... Figure 3 As shown, the terminal includes a processor 10 and a memory 20. Figure 3 Only some of the terminal components are shown; however, it should be understood that it is not required to implement all of the components shown, and more or fewer components may be implemented instead.

[0144] In some embodiments, the memory 20 may be an internal storage unit of the terminal, such as the terminal's hard drive or memory. In other embodiments, the memory 20 may also be an external storage device of the terminal, such as a plug-in hard drive or smart memory card equipped on the terminal. SmartMediaCard , SMC ), Secure Digital ( SecureDigital , SD ) card, flash memory card ( FlashCard Furthermore, the memory 20 may include both internal storage units and external storage devices of the terminal. The memory 20 is used to store application software and various types of data installed on the terminal. The memory 20 can also be used to temporarily store data that has been output or will be output. In one embodiment, the memory 20 stores a kinematic semi-analytical modeling program 30 for a parallel mechanism of a human wrist, which can be executed by the processor 10 to implement the kinematic semi-analytical modeling method for a parallel mechanism of a human wrist in this application.

[0145] In some embodiments, the processor 10 may be a central processing unit (CPU). Central Processing Unit , CPU (a microprocessor or other chip) is used to run program code stored in the memory 20 or process data, such as executing a kinematic semi-analytical modeling method for the parallel mechanism of the humanoid wrist.

[0146] In one embodiment, when processor 10 executes kinematic semi-analytical modeling program 30 of parallel mechanism of human wrist in memory 20, the following steps are performed:

[0147] Obtain a global coordinate system, a first coordinate system, and a second coordinate system. The global coordinate system is the overall coordinate system of the parallel mechanism of the humanoid wrist. The origin of the first coordinate system is the rotation center of the first rotary joint of the parallel mechanism of the humanoid wrist. z The axis coincides with the rotation axis of the first rotary joint; the origin of the second coordinate system is the rotation center of the second rotary joint of the parallel mechanism of the anthropomorphic wrist, and the second coordinate system... z The shaft coincides with the rotation axis of the second rotary joint;

[0148] Obtain the target corresponding to the end-effector pose of the parallel mechanism of the humanoid wrist. D - H The expression, the target D - H The expression illustrates the relationship between the end-effector pose and the first joint angle and the second joint angle, where the first joint angle is the angle of the third branch of the parallel mechanism of the anthropomorphic wrist around the first coordinate system. zThe angle of rotation of the axis, the second joint angle is the angle of rotation of the third branch around the second coordinate system. z The angle of axis rotation, wherein the third branch is used to connect the active drive branch of the parallel mechanism of the humanoid wrist and the moving platform of the parallel mechanism of the humanoid wrist, and the active drive branch includes the first branch and the second branch.

[0149] Obtain the target module length expression, which shows the relationship between the first module length and the second module length and the first joint angle and the second joint angle. The first module length is the module length of the first vector in the global coordinate system, and the second module length is the module length of the second vector in the global coordinate system. The first vector is the vector representation of the first branch, and the second vector is the vector representation of the second branch.

[0150] Obtain the values ​​of the first module length and the second module length, and substitute these values ​​into the target. D - H The expression and the target module length expression are used to obtain the end pose.

[0151] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A kinematic semi-analytical modeling method of a humanoid wrist parallel mechanism, applied to a humanoid wrist parallel mechanism, characterized in that, The humanoid wrist parallel mechanism comprises a support, a first branch chain, a second branch chain, a third branch chain and a moving platform; The first branch chain and the second branch chain each comprise a front end spherical pair, a moving pair and a rear end spherical pair, the front end spherical pairs of the first branch chain and the second branch chain are connected with the support, the rear end spherical pairs of the first branch chain and the second branch chain are connected with the third branch chain, wherein the moving pairs of the first branch chain and the second branch chain are active driving parts; the third branch chain comprises a first rotating pair and a second rotating pair, the second rotating pair is connected with the moving platform, and the rotation center of the second rotating pair is the geometric center of the moving platform; The moving platform is the output terminal of the humanoid wrist parallel mechanism; When kinematic forward solution of the humanoid wrist parallel mechanism is performed, the following steps are included: obtaining a global coordinate system, a first coordinate system and a second coordinate system, wherein the global coordinate system is a total coordinate system of the parallel mechanism of the humanoid wrist, an origin of the first coordinate system is a rotation center of a first rotation pair of the parallel mechanism of the humanoid wrist, and a z axis of the first coordinate system coincides with a rotation axis of the first rotation pair; an origin of the second coordinate system is a rotation center of a second rotation pair of the parallel mechanism of the humanoid wrist, and a z axis of the second coordinate system coincides with a rotation axis of the second rotation pair; acquire a target corresponding to an end position and posture of a parallel mechanism of the anthropomorphic wrist D - H expression, the target D - H The expression shows the relationship between the end position and posture and the first joint angle, the second joint angle, the first joint angle being the angle of rotation of the third branch chain of the parallel mechanism of the anthropomorphic wrist around the z axis of the first coordinate system, the second joint angle being the angle of rotation of the third branch chain around the z axis of the second coordinate system, wherein the third branch chain is used to connect a driven branch chain of the parallel mechanism of the anthropomorphic wrist and a moving platform of the parallel mechanism of the anthropomorphic wrist, and the driven branch chain comprises a first branch chain and a second branch chain; A target module length expression is obtained, the target module length expression shows the relationship between a first module length and a second module length and the first joint angle and the second joint angle, the first module length is the module length of a first vector in the global coordinate system, the second module length is the module length of a second vector in the global coordinate system, the first vector is a vector representation of the first branch chain, and the second vector is a vector representation of the second branch chain; obtaining values for the first mode length and the second mode length, and bringing the values for the first mode length and the second mode length into the target D - H expression and the target mode length expression to obtain the end pose.

2. The kinematic semi-analytical modeling method of a humanoid wrist parallel mechanism according to claim 1, characterized in that, The target D - H The expression is: ； wherein, denotes the global coordinate system, is the end pose, denoting the position and pose of the moving platform with respect to the global coordinate system, denotes , denotes , denotes the distance between the axes of the first and second revolute pairs measured along the direction of the second coordinate system's x axis, is the first joint angle, is the second joint angle.

3. The kinematic semi-analytical modeling method of a humanoid wrist parallel mechanism according to claim 2, characterized in that, The target module length expression is obtained based on the first vector expression, the second vector expression, the first relationship expression and the second relationship expression. based on the target D - H The expression obtains a first vector expression and a second vector expression, the first vector expression showing a relationship between the first vector and the first joint angle and the second joint angle, and the second vector expression showing a relationship between the second vector and the first joint angle and the second joint angle; The first vector expression is: The second vector expression is:

4. The kinematic semi-analytical modeling method of a humanoid wrist parallel mechanism according to claim 3, characterized in that, The method includes determining a target based on the target D - H The expression obtains a first vector expression and a second vector expression, including: based on the target D - H expression acquisition A point, B point, C point and D point in the global coordinate system, wherein the A point is the center point of the spherical pair connected by the first branch chain and the support of the parallel mechanism of the humanoid wrist, the B point is the center point of the spherical pair connected by the second branch chain and the support of the parallel mechanism of the humanoid wrist, the C point is the center point of the spherical pair connected by the first branch chain and the third branch chain, and the D point is the center point of the spherical pair connected by the second branch chain and the third branch chain. based on the A point and the C position matrix of the point in the global coordinate system results in the first vector expression; based on the B point and the D position matrix of the points in the global coordinate system results in the second vector expression.

5. The kinematic semi-analytical modeling method of a humanoid wrist parallel mechanism according to claim 4, characterized in that, The target D - H Expression acquisition A Point, B Point, C Point and D Point position matrix in the global coordinate system, comprising: The A The position matrix of the point in the global coordinate system is: ； The B The position matrix of the point in the global coordinate system is: ； The C The position matrix of the point in the global coordinate system is: ； in, , for the C The position matrix of the point in the second coordinate system; The D The position matrix of the point in the global coordinate system is: ； wherein is the position matrix of the point in the second coordinate system, and D is the position matrix of the point in the second coordinate system, and ; .

6. The kinematic semi-analytical modeling method of a humanoid wrist parallel mechanism according to claim 5, characterized in that, The first relationship expression is: ； The second relationship expression is: 。 7. The kinematic semi-analytical modeling method of a humanoid wrist parallel mechanism according to claim 6, characterized in that, The target module length expression is obtained based on the first vector expression, the second vector expression, the first relationship expression and the second relationship expression, including: ； A first intermediate relationship expression is obtained based on the first relationship expression and the second relationship expression; ； wherein denotes the first mode length, denotes the second mode length.

8. The kinematic semi-analytical modeling method of a humanoid wrist parallel mechanism according to claim 7, characterized in that, The first intermediate relationship expression is optimized to obtain a second intermediate relationship expression: The target module length expression is obtained based on the second intermediate relationship expression; The first intermediate relationship expression is: The second intermediate relationship expression is: The target module length expression is obtained based on the second intermediate relationship expression, including: ； ； The second intermediate relationship expression is adjusted based on a target constant coefficient to obtain the target module length expression; ； 。 9. The kinematic semi-analytical modeling method of a humanoid wrist parallel mechanism according to claim 8, characterized in that, The target module length expression is: The terminal comprises a processor, a computer readable storage medium in communication connection with the processor, the computer readable storage medium is adapted to store a plurality of instructions, and the processor is adapted to call the instructions in the computer readable storage medium to perform the steps of the kinematic semi-analytical modeling method of the humanoid wrist parallel mechanism according to any one of the above claims 1-9. ​ ； wherein is the target constant coefficient, and: ； ； ； ； ； ； 。 10. A terminal, characterized by comprising: ​

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